Thanks Johannes,

I am working with risky and stochastic steady state concept and getting the right covariance matrix is essential to what i am trying to do.

- So in dynare code if i have the following entries

**Z1=C(+1)^-(rho);**

**Z2=Z1*Z1(+1);**

these in dynare are interpreted as:

1-) Z1_{t}=\mathbb{E}_{t} [C_{t+1}^{ -\rho}]

2-) Z2_{t}=\mathbb{E}_{t} [C_{t+1}^{ -\rho}\mathbb{E}_{t} [C_{t+2}^{ -\rho}] ]=\mathbb{E}_{t} [C_{t+1}^{ -\rho}]\mathbb{E}_{t} [C_{t+2}^{ -\rho}] OR

2a-) Z2_{t}=\mathbb{E}_{t} [C_{t+1}^{ -\rho}C_{t+2}^{ -\rho} ] i believe this is wrong but not 100% sure

3-)**Z1(+1)** means \mathbb{E}_{t+1}[Z1_{t+1 }]=\mathbb{E}_{t+1} [C_{t+2}^{ -\rho}]

4-)**Z2(+1)** means \mathbb{E}_{t+1}[Z2_{t+1 }]=\mathbb{E}_{t+1}[\mathbb{E}_{t+1}[C_{t+2}^{ -\rho}]*\mathbb{E}_{t+1}[C_{t+3}^{ -\rho}]] =\mathbb{E}_{t+1}[C_{t+2}^{ -\rho}]\mathbb{E}_{t+1}[C_{t+3}^{ -\rho}] OR

4a-) \mathbb{E}_{t+1}[Z2_{t+1 }]=\mathbb{E}_{t+1}[C_{t+2}^{ -\rho}C_{t+3}^{ -\rho}] this i believe is wrong but again not %100 sure

- But instead if i define the auxiliary variable as

**Z1=C^-(rho);**

**Z2=Z1*Z1(+1);**

then

5-) \mathbb{E}_{t}[Z1_{t}]=\mathbb{E}_{t} [C_{t}^{ -\rho}] expectations operators drop so Z1_{t}=C_{t}^{ -\rho} and

6-) **Z1(+1)** means Z1_{t+1}=C_{t+1}^{ -\rho} without expections

7-) **Z2** means Z2_{t}=\mathbb{E}_{t} [C_{t}^{ -\rho}C_{t+1}^{ -\rho} ]

8 -) **Z2(+1)** means \mathbb{E}_{t+1}[Z2_{t+1 }]=\mathbb{E}_{t+1}[C_{t+1}^{ -\rho}C_{t+2}^{ -\rho}]

and the auxiliary variable Z1 enters without expectations operator because in the initial setup **Z1=C^-(rho);** is defined in a way that it holds in every period exactly

thanks a lot again and hopefully the way i described it is not confusing

regards